There are thousands of alphabet books and most of them are the same book: twenty-six pages, one picture each, A is for apple. That is not a criticism exactly. A child does need to meet the letters, and a simple book does that.
But a few do something else, and those are the ones that survive being read forty times. Here are the ones I would actually put in a house, including some that compete directly with mine, because a list of one is not a list.
Dr. Seuss's ABC
Still the best introduction to the sounds rather than the names, which is the thing that matters for reading. It is relentless, it is nonsense, and a four-year-old will have it memorised inside a week. Buy it first if you are buying one book.
Chicka Chicka Boom Boom
The letters climb a coconut tree and fall out of it. It has a rhythm you cannot read slowly even if you try, and children who will not sit still will sit still for this. Its weakness is that it teaches letter names, not sounds, so it pairs better with the Seuss than it stands alone.
Anything by Julia Donaldson, even the ones that are not alphabet books
Not an alphabet book, and I am putting it on the list anyway. If you want a child to love rhyme, Donaldson is the shortest road there is, and a child who loves rhyme learns letters faster than a child who has been taught letters. The Gruffalo and Room on the Broom are the obvious two.
An alphabet frieze on the wall
Not a book. Costs almost nothing, and it does something no book does, which is sit there all year at eye level being available. Children point at things on walls. They rarely point at things in a closed book.
A photograph album with the letters written in
The homemade option, and the one that works best of all with a three or four-year-old. Their own photographs, one letter written next to each. Nothing has ever competed with a child's own face for a child's attention.
Books where the animal has a personality
This is where the category starts getting interesting. An alphabet where each letter is a character rather than an object gives a child something to remember the letter by, and personality is stickier than objects.
And mine, since you are on my website
Sing Me a Fable is twenty-six fables in rhyme, one animal and one character fault per letter, from Aggression to Zealotry. Each has a song, a karaoke video and a game.
Its honest weakness compared to the books above: it is longer, and a four-verse fable is more than a two-year-old will sit through. Its honest strength: it lasts. A three-year-old grows out of A is for apple by four. Nobody grows out of a story about a boy who cried wolf.
What I would actually do
Buy the Seuss. Put a frieze on the wall. Make the photograph album on a Sunday.
Then, when the child is four or five and the simple books have stopped holding them, that is the moment for the longer thing.
If you want to test that with no money down, the twenty-six colouring posters are free, one animal per letter.